×

zbMATH — the first resource for mathematics

Solution of nonlinear boundary value problems in weighted Sobolev spaces. (English) Zbl 0707.46022
Problems and methods in mathematical physics, Proc. 9th Conf., TMP, Karl- Marx-Stadt/GDR 1988, Teubner-Texte Math. 111, 130-137 (1989).
[For the entire collection see Zbl 0675.00020.]
This paper is a discussion, without proofs, of the use of weighted Sobolev spaces in the study of weak solutions of linear and nonlinear elliptic boundary-value problems with degenerate or singular coefficients. This approach is pedagogical, and many illustrative examples are given. The approach seems to be via monotone operators.
Reviewer: J.F.Toland

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J40 Boundary value problems for higher-order elliptic equations
35J60 Nonlinear elliptic equations
Citations:
Zbl 0675.00020